Nonlinear vibration analysis of thermo-hyperelastic cylindrical shells under combined excitations

With the widespread application of hyperelastic materials in flexible structures and smart soft materials, the nonlinear dynamic behavior of thermo-hyperelastic cylindrical shells in thermal environments has attracted increasing attention. In this paper, the nonlinear resonant responses and complex dynamic behaviors of thermo-hyperelastic cylindrical shells subjected to combined axial and radial harmonic excitations and thermal effects are investigated. The nonlinear governing equations of motion are established based on the modified Donnell shell theory, the eight-chain non-Gaussian network model, and the Lagrange equation. The frequency-response curves and force-amplitude response curves are obtained using the harmonic balance method in conjunction with the pseudo-arc length continuation method. The effects of relevant parameters on the natural frequencies, vibration amplitudes, and chaotic response characteristics of the structure are analyzed. The results indicate that the natural frequencies of the thermo-hyperelastic cylindrical shell gradually increase with increasing temperature difference, thickness-radius ratio, and radius-length ratio. The axial and radial frequency-response curves exhibit typical hardening characteristics and jump phenomena under various parameter conditions, and different parameters show distinct influences on the nonlinear responses of the system. Compared with other parameters, the influence of temperature difference on the vibration amplitude is relatively weak. The phase difference has a more significant effect on the axial response. In addition, the system undergoes transitions among periodic, quasi-periodic, and chaotic motions as the parameters vary, exhibiting rich and complex nonlinear dynamic response behaviors. • A thermo-hyperelastic shell model with axial and radial excitations is established. • Hardening responses, jump phenomena, and multi-valued regions are revealed. • Resonance peaks and hardening behaviors are shifted with geometric ratios. • Stronger effects of phase difference on axial resonance responses are identified. • Alternating occurrences of periodic and chaotic motions are observed.